Abstract
The parity-deformations of the quantum harmonic oscillator are used to describe the generalized Jaynes-Cummings model based on the λ-analog of the Heisenberg algebra. The behavior is interestingly that of a coupled system comprising a two-level atom and a cavity field assisted by a continuous external classical field. The dynamical characters of the system is explored under the influence of the external field. In particular, we analytically study the generation of robust and maximally entangled states formed by a two-level atom trapped in a lossy cavity interacting with an external centrifugal field. We investigate the influence of deformation and detuning parameters on the degree of the quantum entanglement and the atomic population inversion. Under the condition of a linear interaction controlled by an external field, the maximally entangled states may emerge periodically along with time evolution. In the dissipation regime, the entanglement of the parity deformed JCM are preserved more with the increase of the deformation parameter, i.e. the stronger external field induces better degree of entanglement.
Highlights
In addition to the above -cited generalizations, in recent years, a lot of interest has been given to to the extension of the boson oscillator algebra
The same R-deformed Heisenberg algebra (RDHA) was used for solving the quantum mechanical Calogero model or pseudo harmonic oscillator (PHO)[37,38,39,40,41]
For an atom initially stated in the upper level, |+〉, the population inversion dynamics are analyzed for a deformed JCM was surrounded by a dissipative environment where the dissipation of the upper-level is considered
Summary
The parity-deformations of the quantum harmonic oscillator are used to describe the generalized Jaynes-Cummings model based on the λ-analog of the Heisenberg algebra. The Jaynes-Cummings model (JCM) which is used extensively in quantum optics describes the interaction of a single quantized radiation field with a two-level atom. The solvability and applications of this model has long been discussed[1,2] This simple model describes various quantum mechanical phenomena, for example, Rabi oscillations[2,3], collapse and revivals of the atomic population inversion[4] and entanglement between atom and field[5]. The same RDHA was used for solving the quantum mechanical Calogero model or pseudo harmonic oscillator (PHO)[37,38,39,40,41] This algebra has been employed for bosonization of super-symmetric quantum mechanics[41,42,43] and for describing anyons in (2 + 1)[42,44] and (l + 1) dimensions[45,46]. Λ ∈ is called Wigner’s deformation parameter and Ris a parity operator with the following properties
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
